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100   $a20231106d2023      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRepresentations of SU(2,1) in Fourier Term Modules /$fby Roelof W. Bruggeman, Roberto J. Miatello
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023.
215   $a1 online resource (217 pages)
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2340
311 08$aPrint version: Bruggeman, Roelof W. Representations of SU(2,1) in Fourier Term Modules Cham : Springer,c2023 9783031431913 
330   $aThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the ?abelian? Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the ?non-abelian? modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v2340
606   $aNumber theory
606   $aFourier analysis
606   $aTopological groups
606   $aLie groups
606   $aNumber Theory
606   $aFourier Analysis
606   $aTopological Groups and Lie Groups
606   $aTeoria de nombres$2thub
606   $aAnàlisi de Fourier$2thub
608   $aLlibres electrònics$2thub
615  0$aNumber theory.
615  0$aFourier analysis.
615  0$aTopological groups.
615  0$aLie groups.
615 14$aNumber Theory.
615 24$aFourier Analysis.
615 24$aTopological Groups and Lie Groups.
615  7$aTeoria de nombres
615  7$aAnàlisi de Fourier
676   $a515.2433
700   $aBruggeman$b Roelof W$056659
701   $aMiatello$b Roberto J$01437763
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996565864703316
996   $aRepresentations of SU(2,1) in Fourier Term Modules$93598646
997   $aUNISA